Abstract. In this article, we inquire about the use of inequalities in the history
of mathematics, so as to help improve the quality of teaching this theme. The
historical analysis of a concept provides clues to interpret the productions,
conceptions, and difficulties of students and to design experiences that favor
From a phenomenological study (Freudenthal, 2002) we characterize mathematical
phenomena that are organized by the concept of inequalities. In this
article, we present some evidence of the manifestation of these phenomena in
the history of mathematics.
We reflect on the type of experiences that are necessary for students, for
them to create “mental objects” of inequality in an elementary stage, that will
enable them to study this advanced mathematics topic, in optimal conditions.